2024/05/15 by Lukas Kölsch, Kölsch, Lukas
Computer Science · #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #Polynomial and algebraic computation #Rings and Algebras (math.RA) #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.2405.09068
openalex publication_date 2024/05/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this article, we present two new constructions for semifields of order p2m. Together, the constructions unify and generalize around a dozen distinct semifield constructions, including both the oldest known construction by Dickson and the largest known construction in odd characteristic by Taniguchi. The constructions also provably yield many new semifields. We give precise conditions when the new semifields we find are equivalent and count precisely how many new inequivalent semifields we construct.